%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT040-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:55:22 AM UTC 2026
% Result : Unsatisfiable 183.15s 183.47s
% Output : Proof 183.29s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__sup__distrib2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib2_0) ).
cnf(cls_wfI__pf_1,axiom,
( c_Wellfounded_Owf(V_R,T_a)
| c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_wfI__pf_1) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Un__absorb_0) ).
cnf(cls_sup__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_Un__Image_0,axiom,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_b,T_a),tc_bool)),V_A,T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_S,V_A,T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Image_0) ).
cnf(cls_Image__Un_0,axiom,
c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Image__Un_0) ).
cnf(cls_tfl__wf__induct_1,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ hBOOL(hAPP(V_P,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(V_P,V_R,T_a)))
| hBOOL(hAPP(V_P,V_Rb)) ),
file('theBenchmark.p',cls_tfl__wf__induct_1) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
file('theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__idemp_0) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
file('theBenchmark.p',cls_doubleton__eq__iff_4) ).
cnf(cls_eq__eqI_1,axiom,
( V_xa = V_y
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( V_x_H = V_y_H
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__empty_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_diff__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__diff__subset_0) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__left__commute_0) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__assoc_0) ).
cnf(cls_sup__assoc_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
cnf(cls_Int__absorb2_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_Int__absorb1_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Int__absorb1_0) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_Un__subset__iff_2,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_2) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__upper2_0) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__upper1_0) ).
cnf(cls_Un__least_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__least_0) ).
cnf(cls_le__supI_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI_0) ).
cnf(cls_sup__ge1_0,axiom,
( c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_sup__ge2_0,axiom,
( c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_sup__least_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__least_0) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_2) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_inf__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_wf__acyclic_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_Wellfounded_Oacyclic(V_r,T_a) ),
file('theBenchmark.p',cls_wf__acyclic_0) ).
cnf(cls_Diff__partition_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Diff__partition_0) ).
cnf(cls_distrib__inf__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_distrib__inf__le_0) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__subset_0) ).
cnf(cls_insert__Diff__single_0,axiom,
c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a),
file('theBenchmark.p',cls_insert__Diff__single_0) ).
cnf(cls_singleton__inject_0,axiom,
( V_a = V_b
| c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) != c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_singleton__inject_0) ).
cnf(cls_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__crazy_0) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__constant__conv_0) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_in(V_x,V_xa,T_a)
| c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
cnf(cls_insert__subset_0,axiom,
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_Sigma__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
cnf(cls_insert__code_2,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
file('theBenchmark.p',cls_insert__code_2) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_2) ).
cnf(cls_subset__insert__iff_1,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_1) ).
cnf(cls_subset__insert_1,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert_1) ).
cnf(cls_subset__insert_0,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_Int__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__Un__distrib_0) ).
cnf(cls_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__Un__distrib2_0) ).
cnf(cls_Domain__Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Domain__Diff__subset_0) ).
cnf(cls_Diff__triv_0,axiom,
( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__triv_0) ).
cnf(cls_singletonE_0,axiom,
( ~ c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_a ),
file('theBenchmark.p',cls_singletonE_0) ).
cnf(cls_Sigma__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
cnf(cls_image__constant_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b) ),
file('theBenchmark.p',cls_image__constant_0) ).
cnf(cls_subset__insert__iff_0,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_0) ).
cnf(cls_subset__insert__iff_3,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_3) ).
cnf(cls_diff__single__insert_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_diff__single__insert_0) ).
cnf(cls_insert__Diff1_0,axiom,
( ~ c_in(V_x,V_B,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__Diff1_0) ).
cnf(cls_insert__subset_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_subset__insertI2_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_b,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insertI2_0) ).
cnf(cls_Range__Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Range__Diff__subset_0) ).
cnf(cls_wf__induct_1,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_wf__induct_1) ).
cnf(cls_inf__compl__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_Compl__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Compl__disjoint_0) ).
cnf(cls_Compl__disjoint2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Compl__disjoint2_0) ).
cnf(cls_rtrancl__Un__subset_0,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
file('theBenchmark.p',cls_rtrancl__Un__subset_0) ).
cnf(cls_empty__is__image_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a) ),
file('theBenchmark.p',cls_empty__is__image_0) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_Un__insert__left_0) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_Un__insert__right_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_le__imp__neg__le_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_Compl__anti__mono_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Compl__anti__mono_0) ).
cnf(cls_Compl__subset__Compl__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
cnf(cls_Compl__subset__Compl__iff_1,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a)
| ~ class_Orderings_Obot(T_a) ),
file('theBenchmark.p',cls_bot__least_0) ).
cnf(cls_Compl__Diff__eq_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Compl__Diff__eq_0) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__insert_0) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__insert2_0) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_insert__not__empty_0) ).
cnf(cls_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_insert__inter__insert_0) ).
cnf(cls_Image__empty_0,axiom,
c_Relation_OImage(V_R,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Image__empty_0) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a),
file('theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_insert__code_0,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| V_y = V_x
| hBOOL(hAPP(V_A,V_x)) ),
file('theBenchmark.p',cls_insert__code_0) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__Compl__self__eq_1) ).
cnf(cls_Domain__insert_0,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)),T_a,T_b) = c_Set_Oinsert(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a),
file('theBenchmark.p',cls_Domain__insert_0) ).
cnf(cls_sym__Un_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_Relation_Osym(V_s,T_a)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_sym__Un_0) ).
cnf(cls_Domain__Int__subset_0,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Domain__Int__subset_0) ).
cnf(cls_inf__bot__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_inf__bot__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_Int__empty__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__empty__left_0) ).
cnf(cls_Int__empty__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__empty__right_0) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__Int__subset_0) ).
cnf(cls_Image__Int__subset_0,axiom,
c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Image__Int__subset_0) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
cnf(cls_Sigma__Diff__distrib1_0,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__cancel_0) ).
cnf(cls_sup1E_0,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(V_B,V_x)) ),
file('theBenchmark.p',cls_sup1E_0) ).
cnf(cls_sup1CI_0,axiom,
( ~ hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_sup1CI_1,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_sup1CI_1) ).
cnf(cls_wf__Un_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_Wellfounded_Owf(V_s,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(V_r,T_a,T_a),c_Relation_ORange(V_s,T_a,T_a),tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_wf__Un_0) ).
cnf(cls_Times__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Times__Int__distrib1_0) ).
cnf(cls_refl__on__Un_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_Relation_Orefl__on(V_B,V_s,T_a)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_refl__on__Un_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__assoc_0) ).
cnf(cls_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__left__commute_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_sup__bot__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
file('theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_empty__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_empty__Diff_0) ).
cnf(cls_insert__times__insert_0,axiom,
c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),tc_prod(T_a,T_b)),
file('theBenchmark.p',cls_insert__times__insert_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('theBenchmark.p',cls_bot1E_0) ).
cnf(cls_Diff__Int__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int__distrib_0) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int__distrib2_0) ).
cnf(cls_image__constant__conv_1,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_Diff__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_D,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__mono_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_trans__Int_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Otrans(V_s,T_a)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_trans__Int_0) ).
cnf(cls_distrib__sup__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_distrib__sup__le_0) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int2_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_wf__def_1,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_xb)) ),
file('theBenchmark.p',cls_wf__def_1) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( V_x = V_y
| c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( V_a = V_b
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( V_A = V_B
| c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)) != c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_acyclic__converse_0,axiom,
( ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Wellfounded_Oacyclic(V_r,T_a) ),
file('theBenchmark.p',cls_acyclic__converse_0) ).
cnf(cls_acyclic__converse_1,axiom,
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_acyclic__converse_1) ).
cnf(cls_inf__sup__absorb_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_Un__Diff__Int_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Un__Diff__Int_0) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_Un__absorb1_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Un__absorb1_0) ).
cnf(cls_Un__absorb2_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Un__absorb2_0) ).
cnf(cls_subset__Un__eq_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != V_B ),
file('theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_refl__on__Int_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_Relation_Orefl__on(V_B,V_s,T_a)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_refl__on__Int_0) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( V_a = V_c
| V_a = V_d
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_0) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( V_a = V_c
| V_b = V_c
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_1) ).
cnf(cls_converse__Int_0,axiom,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_converse__Int_0) ).
cnf(cls_Int__insert__right_1,axiom,
( c_in(V_a,V_A,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__insert__right_1) ).
cnf(cls_Int__insert__left_1,axiom,
( c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_strict__linear__order__on__def_2,axiom,
( ~ c_Order__Relation_Ostrict__linear__order__on(V_A,V_r,T_a)
| c_Relation_Ototal__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_strict__linear__order__on__def_2) ).
cnf(cls_Un__empty_1,axiom,
( V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__empty_1) ).
cnf(cls_Un__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__empty_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( V_B = c_Orderings_Obot__class_Obot(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Diff__cancel2_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_rel__comp__distrib2_0,axiom,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_rel__comp__distrib2_0) ).
cnf(cls_rel__comp__distrib_0,axiom,
c_Relation_Orel__comp(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_rel__comp__distrib_0) ).
cnf(cls_Int__subset__iff_1,axiom,
( ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_1) ).
cnf(cls_Int__subset__iff_0,axiom,
( ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_0) ).
cnf(cls_le__infE_0,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infE_0) ).
cnf(cls_le__infE_1,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infE_1) ).
cnf(cls_le__infI1_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI1_0) ).
cnf(cls_le__infI2_0,axiom,
( ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI2_0) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_0) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_1) ).
cnf(cls_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Diff_0) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_inf__eq__neg__sup_0) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_Compl__Int_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Compl__Int_0) ).
cnf(cls_compl__inf_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_compl__inf_0) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_neg__inf__eq__sup_0) ).
cnf(cls_Domain__Un__eq_0,axiom,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Domain__Un__eq_0) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_insert__is__Un_0) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__left__absorb_0) ).
cnf(cls_sup__left__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a),
file('theBenchmark.p',cls_empty__is__image_1) ).
cnf(cls_Compl__Un_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Compl__Un_0) ).
cnf(cls_compl__sup_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_neg__sup__eq__inf_0) ).
cnf(cls_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_Range__Int__subset_0,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Range__Int__subset_0) ).
cnf(cls_wf__induct__rule_1,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_wf__induct__rule_1) ).
cnf(cls_rtrancl__Un__rtrancl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
file('theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
cnf(cls_Diff__Compl_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Compl_0) ).
cnf(cls_insert__Diff__if_1,axiom,
( c_in(V_x,V_B,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_x,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_insert__Diff__if_1) ).
cnf(cls_subset__insert__iff_4,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_4) ).
cnf(cls_inf1E_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_B,V_x)) ),
file('theBenchmark.p',cls_inf1E_1) ).
cnf(cls_inf1E_0,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x)) ),
file('theBenchmark.p',cls_inf1E_0) ).
cnf(cls_Range__insert_0,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)),T_b,T_a) = c_Set_Oinsert(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a),
file('theBenchmark.p',cls_Range__insert_0) ).
cnf(cls_disjoint__eq__subset__Compl_1,axiom,
( ~ c_lessequals(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
cnf(cls_disjoint__eq__subset__Compl_0,axiom,
( c_lessequals(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
cnf(cls_sym__Int_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_Relation_Osym(V_s,T_a)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_sym__Int_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( c_in(V_x,V_A,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_Diff__subset__conv_1,axiom,
( ~ c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__subset__conv_1) ).
cnf(cls_Diff__subset__conv_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__subset__conv_0) ).
cnf(cls_cuts__eq_2,axiom,
( c_Recdef_Ocut(V_f,V_r,V_x,T_a,T_b) = c_Recdef_Ocut(V_g,V_r,V_x,T_a,T_b)
| hAPP(V_f,c_List_Osko__Recdef__Xcuts__eq__1__1(V_f,V_g,V_r,V_x,T_a,T_b)) != hAPP(V_g,c_List_Osko__Recdef__Xcuts__eq__1__1(V_f,V_g,V_r,V_x,T_a,T_b)) ),
file('theBenchmark.p',cls_cuts__eq_2) ).
cnf(cls_double__complement_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_double__complement_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_double__compl_0) ).
cnf(cls_equation__minus__iff_0,axiom,
( V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_acyclic__insert_0,axiom,
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_Wellfounded_Oacyclic(V_r,T_a) ),
file('theBenchmark.p',cls_acyclic__insert_0) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_le__minus__iff_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_minus__le__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_Int__iff_2,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_IntI_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_IntI_0) ).
cnf(cls_insert__iff_2,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
file('theBenchmark.p',cls_insert__iff_2) ).
cnf(cls_insertCI_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_B,T_a),T_a) ),
file('theBenchmark.p',cls_insertCI_0) ).
cnf(cls_UnCI_1,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_UnCI_1) ).
cnf(cls_UnCI_0,axiom,
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_UnCI_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_ball__empty_0,axiom,
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_ball__empty_0) ).
cnf(cls_empty__iff_0,axiom,
~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_emptyE_0,axiom,
~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_emptyE_0) ).
cnf(cls_insertE_0,axiom,
( ~ c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| V_a = V_b
| c_in(V_a,V_A,T_a) ),
file('theBenchmark.p',cls_insertE_0) ).
cnf(cls_UnE_0,axiom,
( ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_UnE_0) ).
cnf(cls_DiffE_1,axiom,
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_DiffE_1) ).
cnf(cls_DiffE_0,axiom,
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_A,T_a) ),
file('theBenchmark.p',cls_DiffE_0) ).
cnf(cls_ComplI_0,axiom,
( c_in(V_c,V_A,T_a)
| c_in(V_c,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_ComplI_0) ).
cnf(cls_ComplD_0,axiom,
( ~ c_in(V_c,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('theBenchmark.p',cls_ComplD_0) ).
cnf(cls_insert__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_insertI1_0,axiom,
c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a),
file('theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insertCI_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
file('theBenchmark.p',cls_insertCI_1) ).
cnf(cls_IntE_1,axiom,
( ~ c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_IntE_1) ).
cnf(cls_IntE_0,axiom,
( ~ c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_A,T_a) ),
file('theBenchmark.p',cls_IntE_0) ).
cnf(cls_bex__empty_0,axiom,
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_Diff__iff_2,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Diff__iff_2) ).
cnf(cls_DiffI_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_DiffI_0) ).
cnf(cls_insert__ident_0,axiom,
( V_A = V_B
| c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a)
| c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_insert__ident_0) ).
cnf(cls_insert__absorb_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Set_Oinsert(V_a,V_A,T_a) = V_A ),
file('theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_eq__equiv__class_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(V_b,V_A,T_a)
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class_0) ).
cnf(cls_equiv__class__eq__iff_3,axiom,
( ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_3) ).
cnf(cls_eq__equiv__class__iff_1,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff_1) ).
cnf(cls_eq__equiv__class__iff_0,axiom,
( c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff_0) ).
cnf(cls_equiv__class__subset_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_lessequals(c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_equiv__class__subset_0) ).
cnf(cls_irrefl__diff__Id_0,axiom,
c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
file('theBenchmark.p',cls_irrefl__diff__Id_0) ).
cnf(cls_rtranclE_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| V_a = V_b
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(V_a,V_b,V_r,T_a),V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtranclE_1) ).
cnf(cls_converse__rtrancl__induct_2,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_b))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(V_P,V_b,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_converse__rtrancl__induct_2) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( V_b = V_d
| V_a = V_d
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_2) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( V_b = V_d
| V_b = V_c
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_3) ).
cnf(cls_subset__empty_0,axiom,
( ~ c_lessequals(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__empty_1) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
file('theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_Int__insert__left_0,axiom,
( ~ c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__insert__left_0) ).
cnf(cls_Int__insert__right_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__insert__right_0) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
file('theBenchmark.p',cls_image__insert_0) ).
cnf(cls_total__on__empty_0,axiom,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_r,T_a),
file('theBenchmark.p',cls_total__on__empty_0) ).
cnf(cls_Un__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__mono_0) ).
cnf(cls_converse__Un_0,axiom,
c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_converse__Un_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
cnf(cls_inf__greatest_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_2) ).
cnf(cls_le__infI_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI_0) ).
cnf(cls_inf__le2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__lower1_0) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_Int__greatest_0,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__greatest_0) ).
cnf(cls_Int__subset__iff_2,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_2) ).
cnf(cls_Times__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Times__Un__distrib1_0) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__distrib_0) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__distrib2_0) ).
cnf(cls_strict__linear__order__on__def_0,axiom,
( ~ c_Order__Relation_Ostrict__linear__order__on(V_A,V_r,T_a)
| c_Relation_Otrans(V_r,T_a) ),
file('theBenchmark.p',cls_strict__linear__order__on__def_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file('theBenchmark.p',cls_insert__code_1) ).
cnf(cls_insert__subset_2,axiom,
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_Times__Diff__distrib1_0,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
file('theBenchmark.p',cls_Times__Diff__distrib1_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_inf__left__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_Range__Un__eq_0,axiom,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Range__Un__eq_0) ).
cnf(cls_wf__Int1_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_r_H,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_wf__Int1_0) ).
cnf(cls_wf__Int2_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(V_r_H,V_r,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_wf__Int2_0) ).
cnf(cls_insert__Diff_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ),
file('theBenchmark.p',cls_insert__Diff_0) ).
cnf(cls_inf__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_1) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__supI2_0,axiom,
( ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_le__supI1_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_le__supE_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supE_1) ).
cnf(cls_le__supE_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supE_0) ).
cnf(cls_Un__subset__iff_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_0) ).
cnf(cls_Un__subset__iff_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_1) ).
cnf(cls_acyclic__subset_0,axiom,
( ~ c_Wellfounded_Oacyclic(V_s,T_a)
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_Wellfounded_Oacyclic(V_r,T_a) ),
file('theBenchmark.p',cls_acyclic__subset_0) ).
cnf(cls_image__is__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(V_f,V_A,T_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_image__is__empty_0) ).
cnf(cls_Int__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__mono_0) ).
cnf(cls_Diff__Un_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Un_0) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__Diff_0) ).
cnf(cls_singleton__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
file('theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( ~ c_lessequals(V_A,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_subset__singletonD_0,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_subset__singletonD_0) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int_0) ).
cnf(cls_inf1I_0,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_inf1I_0) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_sup__eq__neg__inf_0) ).
cnf(cls_double__diff_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_HOL_Ominus__class_Ominus(V_B,c_HOL_Ominus__class_Ominus(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_double__diff_0) ).
cnf(cls_le__eqI_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_le__eqI_1,axiom,
( ~ c_lessequals(V_y_H,V_x_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_insert__mono_0,axiom,
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__empty_2) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__Un_0) ).
cnf(cls_strict__linear__order__on__def_1,axiom,
( ~ c_Order__Relation_Ostrict__linear__order__on(V_A,V_r,T_a)
| c_Relation_Oirrefl(V_r,T_a) ),
file('theBenchmark.p',cls_strict__linear__order__on__def_1) ).
cnf(cls_acyclic__insert_2,axiom,
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('theBenchmark.p',cls_acyclic__insert_2) ).
cnf(cls_acyclic__insert_1,axiom,
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_acyclic__insert_1) ).
cnf(cls_converse__rtrancl__induct_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_b))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(V_P,V_b,V_r,T_a),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(V_P,V_b,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_converse__rtrancl__induct_0) ).
cnf(cls_rtrancl__induct_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_a))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(V_P,V_a,V_r,T_a),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(V_P,V_a,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_b)) ),
file('theBenchmark.p',cls_rtrancl__induct_1) ).
cnf(cls_equiv__class__self_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),T_a) ),
file('theBenchmark.p',cls_equiv__class__self_0) ).
cnf(cls_equiv__class__nondisjoint_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(V_x,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool)),T_a)
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
cnf(cls_insert__image_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_insert__image_0) ).
cnf(cls_Image__singleton__iff_0,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a),T_a)
| c_in(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_Image__singleton__iff_0) ).
cnf(cls_Image__singleton__iff_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_b,c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a),T_a) ),
file('theBenchmark.p',cls_Image__singleton__iff_1) ).
cnf(cls_Times__eq__cancel2_0,axiom,
( V_A = V_B
| ~ c_in(V_x,V_C,T_a)
| c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a) != c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a) ),
file('theBenchmark.p',cls_Times__eq__cancel2_0) ).
cnf(cls_wf__insert_0,axiom,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| c_Wellfounded_Owf(V_r,T_a) ),
file('theBenchmark.p',cls_wf__insert_0) ).
cnf(cls_ImageE_1,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(V_A,V_b,V_r,T_b,T_a),V_A,T_b) ),
file('theBenchmark.p',cls_ImageE_1) ).
cnf(cls_in__rtrancl__UnI_0,axiom,
( ~ c_in(V_x,c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(V_x,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_in__rtrancl__UnI_0) ).
cnf(cls_in__rtrancl__UnI_1,axiom,
( ~ c_in(V_x,c_Transitive__Closure_Ortrancl(V_S,T_a),tc_prod(T_a,T_a))
| c_in(V_x,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_in__rtrancl__UnI_1) ).
cnf(cls_equiv__class__eq_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq_0) ).
cnf(cls_equiv__class__eq__iff_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_0) ).
cnf(cls_acc__induct__rule_0,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a)
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct__rule_0) ).
cnf(cls_not__acc__down_1,axiom,
( c_in(V_x,c_Wellfounded_Oacc(V_R,T_a),T_a)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(V_R,V_x,T_a),c_Wellfounded_Oacc(V_R,T_a),T_a) ),
file('theBenchmark.p',cls_not__acc__down_1) ).
cnf(cls_acc__induct__rule_2,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct__rule_2) ).
cnf(cls_wf__union__merge_0,axiom,
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_R,T_a,T_a,T_a),c_Relation_Orel__comp(V_S,V_R,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_wf__union__merge_0) ).
cnf(cls_wf__union__merge_1,axiom,
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_R,T_a,T_a,T_a),c_Relation_Orel__comp(V_S,V_R,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_wf__union__merge_1) ).
cnf(cls_trancl__unfold_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
file('theBenchmark.p',cls_trancl__unfold_0) ).
cnf(cls_rtrancl__reflcl__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_R,T_a),
file('theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
file('theBenchmark.p',cls_rtrancl__reflcl_0) ).
cnf(cls_rtrancl__r__diff__Id_0,axiom,
c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a),
file('theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
cnf(cls_acyclic__impl__antisym__rtrancl_0,axiom,
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
cnf(cls_sym__Un__converse_0,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
file('theBenchmark.p',cls_sym__Un__converse_0) ).
cnf(cls_sym__Int__converse_0,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
file('theBenchmark.p',cls_sym__Int__converse_0) ).
cnf(cls_trans__reflclI_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_trans__reflclI_0) ).
cnf(cls_Image__Id__on_0,axiom,
c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Image__Id__on_0) ).
cnf(cls_antisym__reflcl_0,axiom,
( ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| c_Relation_Oantisym(V_r,T_a) ),
file('theBenchmark.p',cls_antisym__reflcl_0) ).
cnf(cls_antisym__reflcl_1,axiom,
( ~ c_Relation_Oantisym(V_r,T_a)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_antisym__reflcl_1) ).
cnf(cls_total__on__diff__Id_0,axiom,
( ~ c_Relation_Ototal__on(V_A,c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| c_Relation_Ototal__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_total__on__diff__Id_0) ).
cnf(cls_total__on__diff__Id_1,axiom,
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| c_Relation_Ototal__on(V_A,c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_total__on__diff__Id_1) ).
cnf(cls_converse__rtrancl__induct_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_b))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(V_P,V_b,V_r,T_a),V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_converse__rtrancl__induct_1) ).
cnf(cls_rtrancl__induct_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_a))
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(V_P,V_a,V_r,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_b)) ),
file('theBenchmark.p',cls_rtrancl__induct_0) ).
cnf(cls_rtrancl__induct_3,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(V_P,V_a,V_r,T_a)))
| hBOOL(hAPP(V_P,V_b)) ),
file('theBenchmark.p',cls_rtrancl__induct_3) ).
cnf(cls_rtrancl_Ocases_0,axiom,
( ~ c_in(c_Pair(V_a1,V_a2,t_a,t_a),c_Transitive__Closure_Ortrancl(V_r,t_a),tc_prod(t_a,t_a))
| V_a2 = V_a1
| c_in(c_Pair(V_a1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(V_a1,V_a2,V_r),t_a,t_a),c_Transitive__Closure_Ortrancl(V_r,t_a),tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_rtrancl_Ocases_0) ).
cnf(cls_rtrancl__induct_2,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_a))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(V_P,V_a,V_r,T_a)))
| hBOOL(hAPP(V_P,V_b)) ),
file('theBenchmark.p',cls_rtrancl__induct_2) ).
cnf(cls_rtrancl_Ocases_1,axiom,
( ~ c_in(c_Pair(V_a1,V_a2,t_a,t_a),c_Transitive__Closure_Ortrancl(V_r,t_a),tc_prod(t_a,t_a))
| V_a2 = V_a1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(V_a1,V_a2,V_r),V_a2,t_a,t_a),V_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_rtrancl_Ocases_1) ).
cnf(cls_converse__rtrancl__induct_3,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ hBOOL(hAPP(V_P,V_b))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(V_P,V_b,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_converse__rtrancl__induct_3) ).
cnf(cls_rtranclE_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| V_a = V_b
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(V_a,V_b,V_r,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtranclE_0) ).
cnf(cls_wf__induct__rule_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_wf__induct__rule_0) ).
cnf(cls_wf__def_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_xa)) ),
file('theBenchmark.p',cls_wf__def_0) ).
cnf(cls_tfl__wf__induct_0,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(c_Pair(V_y,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(V_P,V_R,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_Ra)) ),
file('theBenchmark.p',cls_tfl__wf__induct_0) ).
cnf(cls_wf__induct_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_wf__induct_0) ).
cnf(cls_irrefl__trancl__rD_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(V_r,T_a),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(V_r,T_a),T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_irrefl__trancl__rD_0) ).
cnf(cls_converse__tranclE_1,axiom,
( ~ c_in(c_Pair(V_x,V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(V_r,V_x,V_z,T_a),V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_converse__tranclE_1) ).
cnf(cls_trancl_Ocases_0,axiom,
( ~ c_in(c_Pair(V_a1,V_a2,t_a,t_a),c_Transitive__Closure_Otrancl(V_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_a1,V_a2,t_a,t_a),V_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_a1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(V_a1,V_a2,V_r),t_a,t_a),c_Transitive__Closure_Otrancl(V_r,t_a),tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_trancl_Ocases_0) ).
cnf(cls_acyclic__def_0,axiom,
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_acyclic__def_0) ).
cnf(cls_tranclE_1,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(V_a,V_b,V_r,T_a),V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclE_1) ).
cnf(cls_tranclE_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(V_a,V_b,V_r,T_a),T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclE_0) ).
cnf(cls_converse__tranclE_0,axiom,
( ~ c_in(c_Pair(V_x,V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(V_r,V_x,V_z,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_converse__tranclE_0) ).
cnf(cls_trancl_Ocases_1,axiom,
( ~ c_in(c_Pair(V_a1,V_a2,t_a,t_a),c_Transitive__Closure_Otrancl(V_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_a1,V_a2,t_a,t_a),V_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(V_a1,V_a2,V_r),V_a2,t_a,t_a),V_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_trancl_Ocases_1) ).
cnf(cls_subset__equiv__class_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_lessequals(c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_b,V_A,T_a)
| c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_subset__equiv__class_0) ).
cnf(cls_rel__compEpair_1,axiom,
( ~ c_in(c_Pair(V_a,V_c,T_a,T_b),c_Relation_Orel__comp(V_r,V_s,T_a,T_c,T_b),tc_prod(T_a,T_b))
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(V_a,V_c,V_r,V_s,T_a,T_b,T_c),V_c,T_c,T_b),V_s,tc_prod(T_c,T_b)) ),
file('theBenchmark.p',cls_rel__compEpair_1) ).
cnf(cls_rel__compEpair_0,axiom,
( ~ c_in(c_Pair(V_a,V_c,T_a,T_b),c_Relation_Orel__comp(V_r,V_s,T_a,T_c,T_b),tc_prod(T_a,T_b))
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(V_a,V_c,V_r,V_s,T_a,T_b,T_c),T_a,T_c),V_r,tc_prod(T_a,T_c)) ),
file('theBenchmark.p',cls_rel__compEpair_0) ).
cnf(cls_IdE_0,axiom,
( ~ c_in(V_p,c_Relation_OId(T_a),tc_prod(T_a,T_a))
| V_p = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(V_p,T_a),c_ATP__Linkup_Osko__Relation__XIdE__1__1(V_p,T_a),T_a,T_a) ),
file('theBenchmark.p',cls_IdE_0) ).
cnf(cls_wfI__pf_0,axiom,
( c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a),c_Relation_OImage(V_R,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a),T_a,T_a),tc_fun(T_a,tc_bool))
| c_Wellfounded_Owf(V_R,T_a) ),
file('theBenchmark.p',cls_wfI__pf_0) ).
cnf(cls_wfE__pf_0,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_lessequals(V_A,c_Relation_OImage(V_R,V_A,T_a,T_a),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_wfE__pf_0) ).
cnf(cls_wf__acc__iff_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(V_r,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_Wellfounded_Owf(V_r,T_a) ),
file('theBenchmark.p',cls_wf__acc__iff_1) ).
cnf(cls_acc__wfI_0,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(V_r,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_Wellfounded_Owf(V_r,T_a) ),
file('theBenchmark.p',cls_acc__wfI_0) ).
cnf(cls_Sigma__mono_1,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(hAPP(V_B,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(V_A,V_B,V_D,T_a,T_b)),hAPP(V_D,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(V_A,V_B,V_D,T_a,T_b)),tc_fun(T_b,tc_bool))
| c_lessequals(c_Product__Type_OSigma(V_A,V_B,T_a,T_b),c_Product__Type_OSigma(V_C,V_D,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
file('theBenchmark.p',cls_Sigma__mono_1) ).
cnf(cls_Image__subset__eq_1,axiom,
( ~ c_lessequals(V_A,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(V_r,T_b,T_a),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool))
| c_lessequals(c_Relation_OImage(V_r,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Image__subset__eq_1) ).
cnf(cls_Image__subset__eq_0,axiom,
( ~ c_lessequals(c_Relation_OImage(V_r,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(V_r,T_b,T_a),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_Image__subset__eq_0) ).
cnf(cls_Id__onE_0,axiom,
( ~ c_in(V_c,c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),V_A,T_a) ),
file('theBenchmark.p',cls_Id__onE_0) ).
cnf(cls_Id__onE_1,axiom,
( ~ c_in(V_c,c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))
| V_c = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),T_a,T_a) ),
file('theBenchmark.p',cls_Id__onE_1) ).
cnf(cls_cuts__eq_1,axiom,
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(V_f,V_g,V_r,V_x,T_a,T_b),V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Recdef_Ocut(V_f,V_r,V_x,T_a,T_b) = c_Recdef_Ocut(V_g,V_r,V_x,T_a,T_b) ),
file('theBenchmark.p',cls_cuts__eq_1) ).
cnf(cls_trancl__subset__Sigma_0,axiom,
( ~ c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_trancl__subset__Sigma_0) ).
cnf(cls_wf__union__compatible_0,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_Wellfounded_Owf(V_S,T_a)
| ~ c_lessequals(c_Relation_Orel__comp(V_R,V_S,T_a,T_a,T_a),V_R,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_wf__union__compatible_0) ).
cnf(cls_trancl__Int__subset_0,axiom,
( ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r,T_a,T_a,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_trancl__Int__subset_0) ).
cnf(cls_equiv__type_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_equiv__type_0) ).
cnf(cls_rel__comp__subset__Sigma_0,axiom,
( ~ c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| ~ c_lessequals(V_s,c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_c,tc_bool),T_b),T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_bool))
| c_lessequals(c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_c,tc_bool),T_a),T_a,T_c),tc_fun(tc_prod(T_a,T_c),tc_bool)) ),
file('theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
cnf(cls_reflcl__trancl_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a),
file('theBenchmark.p',cls_reflcl__trancl_0) ).
cnf(cls_trancl__reflcl_0,axiom,
c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a),
file('theBenchmark.p',cls_trancl__reflcl_0) ).
cnf(cls_Nitpick_Ortrancl__def_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
file('theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
cnf(cls_refl__on__def_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_refl__on__def_0) ).
cnf(cls_rtrancl__unfold_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(T_a),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
file('theBenchmark.p',cls_rtrancl__unfold_0) ).
cnf(cls_Range__def__raw_0,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(c_Relation_Oconverse(v_r,t_a,t_b),t_b,t_a),
file('theBenchmark.p',cls_Range__def__raw_0) ).
cnf(cls_irrefl__def_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Relation_Oirrefl(V_r,T_a) ),
file('theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_Id__on__subset__Times_0,axiom,
c_lessequals(c_Relation_OId__on(V_A,T_a),c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
file('theBenchmark.p',cls_Id__on__subset__Times_0) ).
cnf(cls_Image__Int__eq_0,axiom,
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(V_R,T_b,T_a),T_a,T_b)
| c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Image__Int__eq_0) ).
cnf(cls_trans__diff__Id_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Oantisym(V_r,T_a)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
file('theBenchmark.p',cls_trans__diff__Id_0) ).
cnf(cls_Nitpick_Orefl_H__def_1,axiom,
( ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(V_r,T_a),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_Nitpick_Orefl_H(V_r,T_a) ),
file('theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
cnf(cls_strict__linear__order__on__def_3,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| c_Order__Relation_Ostrict__linear__order__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_strict__linear__order__on__def_3) ).
cnf(cls_ImageE_0,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(V_A,V_b,V_r,T_b,T_a),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_ImageE_0) ).
cnf(cls_not__acc__down_0,axiom,
( c_in(V_x,c_Wellfounded_Oacc(V_R,T_a),T_a)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(V_R,V_x,T_a),V_x,T_a,T_a),V_R,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_not__acc__down_0) ).
cnf(cls_acc__induct__rule_1,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct__rule_1) ).
cnf(cls_wf__insert_1,axiom,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_wf__insert_1) ).
cnf(cls_wf__insert_2,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('theBenchmark.p',cls_wf__insert_2) ).
cnf(cls_Times__subset__cancel2_1,axiom,
( ~ c_in(V_x,V_C,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool))
| c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool)) ),
file('theBenchmark.p',cls_Times__subset__cancel2_1) ).
cnf(cls_Times__subset__cancel2_0,axiom,
( ~ c_in(V_x,V_C,T_a)
| ~ c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_Times__subset__cancel2_0) ).
cnf(cls_Sigma__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(V_A,V_B,V_D,T_a,T_b),V_A,T_a)
| c_lessequals(c_Product__Type_OSigma(V_A,V_B,T_a,T_b),c_Product__Type_OSigma(V_C,V_D,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
file('theBenchmark.p',cls_Sigma__mono_0) ).
cnf(cls_Image__subset_0,axiom,
( ~ c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| c_lessequals(c_Relation_OImage(V_r,V_C,T_a,T_b),V_B,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_Image__subset_0) ).
cnf(cls_rtrancl__Int__subset_0,axiom,
( ~ c_lessequals(c_Relation_OId(T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r,T_a,T_a,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_rtrancl__Int__subset_0) ).
cnf(cls_trancl__subset__Sigma__aux_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_lessequals(V_r,c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| V_a = V_b
| c_in(V_a,V_A,T_a) ),
file('theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
cnf(cls_refl__on__comp__subset_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| c_lessequals(V_r,c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_refl__on__comp__subset_0) ).
cnf(cls_tranclD_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(V_R,V_x,V_y,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclD_0) ).
cnf(cls_tranclD2_1,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(V_R,V_x,V_y,T_a),V_y,T_a,T_a),V_R,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclD2_1) ).
cnf(cls_trans__O__subset_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| c_lessequals(c_Relation_Orel__comp(V_r,V_r,T_a,T_a,T_a),V_r,tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_trans__O__subset_0) ).
cnf(cls_trancl__mono_0,axiom,
( ~ c_in(V_p,c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_in(V_p,c_Transitive__Closure_Otrancl(V_s,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__mono_0) ).
cnf(cls_image__subset__iff_0,axiom,
( ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_b)
| c_in(hAPP(V_f,V_x),V_B,T_a) ),
file('theBenchmark.p',cls_image__subset__iff_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_Image__mono_0,axiom,
( ~ c_lessequals(V_r_H,V_r,tc_fun(tc_prod(T_a,T_b),tc_bool))
| ~ c_lessequals(V_A_H,V_A,tc_fun(T_a,tc_bool))
| c_lessequals(c_Relation_OImage(V_r_H,V_A_H,T_a,T_b),c_Relation_OImage(V_r,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_Image__mono_0) ).
cnf(cls_subset__image__iff_2,axiom,
( c_lessequals(c_Set_Oimage(V_f,V_x,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_x,V_A,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_subset__image__iff_2) ).
cnf(cls_image__mono_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__mono_0) ).
cnf(cls_Domain__mono_0,axiom,
( ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_b),tc_bool))
| c_lessequals(c_Relation_ODomain(V_r,T_a,T_b),c_Relation_ODomain(V_s,T_a,T_b),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Domain__mono_0) ).
cnf(cls_single__valued__subset_0,axiom,
( ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_b),tc_bool))
| ~ c_Relation_Osingle__valued(V_s,T_a,T_b)
| c_Relation_Osingle__valued(V_r,T_a,T_b) ),
file('theBenchmark.p',cls_single__valued__subset_0) ).
cnf(cls_rev__predicate1D_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(V_Q,V_x)) ),
file('theBenchmark.p',cls_rev__predicate1D_0) ).
cnf(cls_antisym__subset_0,axiom,
( ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_Relation_Oantisym(V_s,T_a)
| c_Relation_Oantisym(V_r,T_a) ),
file('theBenchmark.p',cls_antisym__subset_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_wf__subset_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_lessequals(V_p,V_r,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_Wellfounded_Owf(V_p,T_a) ),
file('theBenchmark.p',cls_wf__subset_0) ).
cnf(cls_predicate1D_0,axiom,
( ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_Q,V_x)) ),
file('theBenchmark.p',cls_predicate1D_0) ).
cnf(cls_subset__trans_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__refl_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_equalityE_0) ).
cnf(cls_order__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_rtrancl__subset__rtrancl_0,axiom,
( ~ c_lessequals(V_r,c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__antisym_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_set__eq__subset_2,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| V_A = V_B ),
file('theBenchmark.p',cls_set__eq__subset_2) ).
cnf(cls_equalityI_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| V_A = V_B ),
file('theBenchmark.p',cls_equalityI_0) ).
cnf(cls_rtrancl__mono_0,axiom,
( ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_rtrancl__mono_0) ).
cnf(cls_rel__comp__mono_0,axiom,
( ~ c_lessequals(V_r_H,V_r,tc_fun(tc_prod(T_a,T_b),tc_bool))
| ~ c_lessequals(V_s_H,V_s,tc_fun(tc_prod(T_b,T_c),tc_bool))
| c_lessequals(c_Relation_Orel__comp(V_r_H,V_s_H,T_a,T_b,T_c),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),tc_fun(tc_prod(T_a,T_c),tc_bool)) ),
file('theBenchmark.p',cls_rel__comp__mono_0) ).
cnf(cls_rtrancl__subset_0,axiom,
( ~ c_lessequals(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(V_S,c_Transitive__Closure_Ortrancl(V_R,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_Transitive__Closure_Ortrancl(V_S,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
file('theBenchmark.p',cls_rtrancl__subset_0) ).
cnf(cls_acc__subset_0,axiom,
( ~ c_lessequals(V_R1,V_R2,tc_fun(tc_prod(T_a,T_a),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(V_R2,T_a),c_Wellfounded_Oacc(V_R1,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_acc__subset_0) ).
cnf(cls_le__funD_0,axiom,
( ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)
| ~ class_HOL_Oord(T_b) ),
file('theBenchmark.p',cls_le__funD_0) ).
cnf(cls_subset__iff_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_t,V_A,T_a)
| c_in(V_t,V_B,T_a) ),
file('theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_set__rev__mp_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_subsetD_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_subsetD_0) ).
cnf(cls_set__mp_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_set__mp_0) ).
cnf(cls_tranclD_1,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(V_R,V_x,V_y,T_a),V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclD_1) ).
cnf(cls_tranclD2_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(V_R,V_x,V_y,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_tranclD2_0) ).
cnf(cls_sym__trans__comp__subset_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_Relation_Otrans(V_r,T_a)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a),V_r,tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('theBenchmark.p',cls_sym__trans__comp__subset_0) ).
cnf(cls_r__into__rtrancl_0,axiom,
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_r__into__rtrancl_0) ).
cnf(cls_r__into__trancl_H_0,axiom,
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_r__into__trancl_H_0) ).
cnf(cls_rtrancl__into__trancl2_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
cnf(cls_rtrancl__into__trancl1_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
cnf(cls_rtrancl__eq__or__trancl_2,axiom,
( V_x = V_y
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
cnf(cls_rtrancl__eq__or__trancl_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| V_x = V_y
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
cnf(cls_rtranclD_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| V_a = V_b
| c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtranclD_0) ).
cnf(cls_rtrancl__converseI_0,axiom,
( ~ c_in(c_Pair(V_y,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__converseI_0) ).
cnf(cls_rtrancl__converseD_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__converseD_0) ).
cnf(cls_single__valued__confluent_0,axiom,
( ~ c_Relation_Osingle__valued(V_r,T_a,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_z,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_z,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_z,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_single__valued__confluent_0) ).
cnf(cls_trancl__into__rtrancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__into__rtrancl_0) ).
cnf(cls_trancl__rtrancl__trancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
cnf(cls_rtrancl__trancl__trancl_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
cnf(cls_trancl__converseD_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__converseD_0) ).
cnf(cls_trancl__converseI_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__converseI_0) ).
cnf(cls_Product__Type_Osplit_0,axiom,
hAPP(c_split(V_f,T_b,T_c,T_a),c_Pair(V_a,V_b,T_b,T_c)) = hAPP(hAPP(V_f,V_a),V_b),
file('theBenchmark.p',cls_Product__Type_Osplit_0) ).
cnf(cls_split__case__cert_0,axiom,
hAPP(c_split(V_f,T_a,T_b,T_c),c_Pair(V_a,V_b,T_a,T_b)) = hAPP(hAPP(V_f,V_a),V_b),
file('theBenchmark.p',cls_split__case__cert_0) ).
cnf(cls_splitD_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_split(V_R,T_a,T_b,tc_fun(T_c,tc_bool)),c_Pair(V_a,V_b,T_a,T_b)),V_c))
| hBOOL(hAPP(hAPP(hAPP(V_R,V_a),V_b),V_c)) ),
file('theBenchmark.p',cls_splitD_H_0) ).
cnf(cls_imageI_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_imageI_0) ).
cnf(cls_image__eqI_0,axiom,
( ~ c_in(V_x,V_A,T_b)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a) ),
file('theBenchmark.p',cls_image__eqI_0) ).
cnf(cls_image__iff_2,axiom,
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| ~ c_in(V_x,V_A,T_b) ),
file('theBenchmark.p',cls_image__iff_2) ).
cnf(cls_rev__image__eqI_0,axiom,
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_aa,T_a),T_a)
| ~ c_in(V_x,V_A,T_aa) ),
file('theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_acc__wfD_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc__wfD_0) ).
cnf(cls_single__valued__Id__on_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(V_A,T_a),T_a,T_a),
file('theBenchmark.p',cls_single__valued__Id__on_0) ).
cnf(cls_sym__trancl_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_sym__trancl_0) ).
cnf(cls_acc__induct_2,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct_2) ).
cnf(cls_trancl__id_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| c_Transitive__Closure_Otrancl(V_r,T_a) = V_r ),
file('theBenchmark.p',cls_trancl__id_0) ).
cnf(cls_acc_Oinducts_2,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ hBOOL(hAPP(V_P,v_sko__Wellfounded__Xacc__Xinducts__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinducts_2) ).
cnf(cls_sym__converse_0,axiom,
( ~ c_Relation_Osym(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Relation_Osym(V_r,T_a) ),
file('theBenchmark.p',cls_sym__converse_0) ).
cnf(cls_sym__converse_1,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| c_Relation_Osym(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_sym__converse_1) ).
cnf(cls_trancl__domain_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a),
file('theBenchmark.p',cls_trancl__domain_0) ).
cnf(cls_Image__iff_0,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(V_A,V_b,V_r,T_b,T_a),V_A,T_b) ),
file('theBenchmark.p',cls_Image__iff_0) ).
cnf(cls_sym__Id_0,axiom,
c_Relation_Osym(c_Relation_OId(T_a),T_a),
file('theBenchmark.p',cls_sym__Id_0) ).
cnf(cls_trans__Id__on_0,axiom,
c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a),
file('theBenchmark.p',cls_trans__Id__on_0) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R,
file('theBenchmark.p',cls_Id__O__R_0) ).
cnf(cls_R__O__Id_0,axiom,
c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R,
file('theBenchmark.p',cls_R__O__Id_0) ).
cnf(cls_antisym__Id__on_0,axiom,
c_Relation_Oantisym(c_Relation_OId__on(V_A,T_a),T_a),
file('theBenchmark.p',cls_antisym__Id__on_0) ).
cnf(cls_wf__converse__trancl_0,axiom,
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),T_a) ),
file('theBenchmark.p',cls_wf__converse__trancl_0) ).
cnf(cls_refl__on__converse_0,axiom,
( ~ c_Relation_Orefl__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Relation_Orefl__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_refl__on__converse_0) ).
cnf(cls_refl__on__converse_1,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| c_Relation_Orefl__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_refl__on__converse_1) ).
cnf(cls_sym__rtrancl_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_sym__rtrancl_0) ).
cnf(cls_wf__comp__self_0,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| c_Wellfounded_Owf(c_Relation_Orel__comp(V_R,V_R,T_a,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_wf__comp__self_0) ).
cnf(cls_wf__comp__self_1,axiom,
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(V_R,V_R,T_a,T_a,T_a),T_a)
| c_Wellfounded_Owf(V_R,T_a) ),
file('theBenchmark.p',cls_wf__comp__self_1) ).
cnf(cls_Image__Id_0,axiom,
c_Relation_OImage(c_Relation_OId(T_a),V_A,T_a,T_a) = V_A,
file('theBenchmark.p',cls_Image__Id_0) ).
cnf(cls_single__valued__Id_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId(T_a),T_a,T_a),
file('theBenchmark.p',cls_single__valued__Id_0) ).
cnf(cls_Domain__Id__on_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A,
file('theBenchmark.p',cls_Domain__Id__on_0) ).
cnf(cls_sym__conv__converse__eq_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| c_Relation_Oconverse(V_r,T_a,T_a) = V_r ),
file('theBenchmark.p',cls_sym__conv__converse__eq_0) ).
cnf(cls_sym__conv__converse__eq_1,axiom,
( c_Relation_Osym(V_r,T_a)
| c_Relation_Oconverse(V_r,T_a,T_a) != V_r ),
file('theBenchmark.p',cls_sym__conv__converse__eq_1) ).
cnf(cls_trancl__range_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a),
file('theBenchmark.p',cls_trancl__range_0) ).
cnf(cls_trans__trancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a),
file('theBenchmark.p',cls_trans__trancl_0) ).
cnf(cls_converse__rel__comp_0,axiom,
c_Relation_Oconverse(c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Relation_Orel__comp(c_Relation_Oconverse(V_s,T_c,T_a),c_Relation_Oconverse(V_r,T_b,T_c),T_a,T_c,T_b),
file('theBenchmark.p',cls_converse__rel__comp_0) ).
cnf(cls_sym__Id__on_0,axiom,
c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a),
file('theBenchmark.p',cls_sym__Id__on_0) ).
cnf(cls_refl__on__Id__on_0,axiom,
c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a),
file('theBenchmark.p',cls_refl__on__Id__on_0) ).
cnf(cls_wf__inv__image_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_Wellfounded_Owf(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_wf__inv__image_0) ).
cnf(cls_r__comp__rtrancl__eq_0,axiom,
c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),
file('theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
cnf(cls_sym__inv__image_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| c_Relation_Osym(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_sym__inv__image_0) ).
cnf(cls_rtrancl__trancl__absorb_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
file('theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
cnf(cls_trans__rtrancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a),
file('theBenchmark.p',cls_trans__rtrancl_0) ).
cnf(cls_trans__converse_0,axiom,
( ~ c_Relation_Otrans(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Relation_Otrans(V_r,T_a) ),
file('theBenchmark.p',cls_trans__converse_0) ).
cnf(cls_trans__converse_1,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| c_Relation_Otrans(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_trans__converse_1) ).
cnf(cls_converse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a),
file('theBenchmark.p',cls_converse__Id_0) ).
cnf(cls_wf__trancl_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_wf__trancl_0) ).
cnf(cls_O__assoc_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b),
file('theBenchmark.p',cls_O__assoc_0) ).
cnf(cls_converse__inv__image_0,axiom,
c_Relation_Oconverse(c_Relation_Oinv__image(V_R,V_f,T_b,T_a),T_a,T_a) = c_Relation_Oinv__image(c_Relation_Oconverse(V_R,T_b,T_b),V_f,T_b,T_a),
file('theBenchmark.p',cls_converse__inv__image_0) ).
cnf(cls_trancl__converse_0,axiom,
c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),
file('theBenchmark.p',cls_trancl__converse_0) ).
cnf(cls_trans__inv__image_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| c_Relation_Otrans(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_trans__inv__image_0) ).
cnf(cls_converse__Id__on_0,axiom,
c_Relation_Oconverse(c_Relation_OId__on(V_A,T_a),T_a,T_a) = c_Relation_OId__on(V_A,T_a),
file('theBenchmark.p',cls_converse__Id__on_0) ).
cnf(cls_comp__equivI_0,axiom,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(V_r,T_a,T_a),V_r,T_a)
| c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a) != V_r ),
file('theBenchmark.p',cls_comp__equivI_0) ).
cnf(cls_antisym__Id_0,axiom,
c_Relation_Oantisym(c_Relation_OId(T_a),T_a),
file('theBenchmark.p',cls_antisym__Id_0) ).
cnf(cls_Range__converse_0,axiom,
c_Relation_ORange(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = c_Relation_ODomain(V_r,T_a,T_b),
file('theBenchmark.p',cls_Range__converse_0) ).
cnf(cls_wf__eq__minimal_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(V_xa,V_Q,T_a)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),V_Q,T_a) ),
file('theBenchmark.p',cls_wf__eq__minimal_0) ).
cnf(cls_Range__Id__on_0,axiom,
c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A,
file('theBenchmark.p',cls_Range__Id__on_0) ).
cnf(cls_single__valued__rel__comp_0,axiom,
( ~ c_Relation_Osingle__valued(V_r,T_a,T_b)
| ~ c_Relation_Osingle__valued(V_s,T_b,T_c)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),T_a,T_c) ),
file('theBenchmark.p',cls_single__valued__rel__comp_0) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r,
file('theBenchmark.p',cls_converse__converse_0) ).
cnf(cls_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(T_a),T_a),
file('theBenchmark.p',cls_trans__Id_0) ).
cnf(cls_equiv__comp__eq_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a) = V_r ),
file('theBenchmark.p',cls_equiv__comp__eq_0) ).
cnf(cls_rtrancl__idemp__self__comp_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
file('theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
cnf(cls_antisym__converse_0,axiom,
( ~ c_Relation_Oantisym(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Relation_Oantisym(V_r,T_a) ),
file('theBenchmark.p',cls_antisym__converse_0) ).
cnf(cls_antisym__converse_1,axiom,
( ~ c_Relation_Oantisym(V_r,T_a)
| c_Relation_Oantisym(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_antisym__converse_1) ).
cnf(cls_acc_Oinduct_2,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ hBOOL(hAPP(V_P,v_sko__Wellfounded__Xacc__Xinduct__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinduct_2) ).
cnf(cls_equiv_Orefl__on_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_Orefl__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_equiv_Orefl__on_0) ).
cnf(cls_rtrancl__converse_0,axiom,
c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a),
file('theBenchmark.p',cls_rtrancl__converse_0) ).
cnf(cls_wfE__min_0,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(V_x,V_Q,T_a)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q,V_R,T_a),V_Q,T_a) ),
file('theBenchmark.p',cls_wfE__min_0) ).
cnf(cls_equiv_Osym_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_Osym(V_r,T_a) ),
file('theBenchmark.p',cls_equiv_Osym_0) ).
cnf(cls_acc_OaccI_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(V_r,V_x,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc_OaccI_1) ).
cnf(cls_congruent2__implies__congruent_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r1,T_a)
| ~ c_Equiv__Relations_Ocongruent2(V_r1,V_r2,V_f,T_a,T_b,T_c)
| ~ c_in(V_a,V_A,T_a)
| c_Equiv__Relations_Ocongruent(V_r2,hAPP(V_f,V_a),T_b,T_c) ),
file('theBenchmark.p',cls_congruent2__implies__congruent_0) ).
cnf(cls_Domain__converse_0,axiom,
c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) = c_Relation_ORange(V_r,T_b,T_a),
file('theBenchmark.p',cls_Domain__converse_0) ).
cnf(cls_trancl__unfold__right_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),
file('theBenchmark.p',cls_trancl__unfold__right_0) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a),
file('theBenchmark.p',cls_trancl__unfold__left_0) ).
cnf(cls_Range__def_0,axiom,
c_Relation_ORange(V_r,T_b,T_a) = c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b),
file('theBenchmark.p',cls_Range__def_0) ).
cnf(cls_total__on__converse_0,axiom,
( ~ c_Relation_Ototal__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
| c_Relation_Ototal__on(V_A,V_r,T_a) ),
file('theBenchmark.p',cls_total__on__converse_0) ).
cnf(cls_total__on__converse_1,axiom,
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| c_Relation_Ototal__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_total__on__converse_1) ).
cnf(cls_equiv_Otrans_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_Otrans(V_r,T_a) ),
file('theBenchmark.p',cls_equiv_Otrans_0) ).
cnf(cls_acc__induct_0,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(V_P,V_r,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a)
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct_0) ).
cnf(cls_d1_I1_J_0,axiom,
v_a____ != v_b____,
file('theBenchmark.p',cls_d1_I1_J_0) ).
cnf(cls_trancl__rtrancl__absorb_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
file('theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
cnf(cls_rtrancl__idemp_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a),
file('theBenchmark.p',cls_rtrancl__idemp_0) ).
cnf(cls_acc_Oinduct_1,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ c_in(c_Pair(V_y,v_sko__Wellfounded__Xacc__Xinduct__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinduct_1) ).
cnf(cls_wfE__min_1,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(V_x,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q,V_R,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
file('theBenchmark.p',cls_wfE__min_1) ).
cnf(cls_RangeE_0,axiom,
( ~ c_in(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(V_b,V_r,T_a,T_b),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_RangeE_0) ).
cnf(cls_acc_OaccI_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(V_r,V_x,T_a),V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc_OaccI_0) ).
cnf(cls_acc__downwards__aux_0,axiom,
( ~ c_in(c_Pair(V_b,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc__downwards__aux_0) ).
cnf(cls_acc__downwards_0,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_b,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc__downwards_0) ).
cnf(cls_acc_Oinducts_0,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ c_in(c_Pair(V_ya,v_sko__Wellfounded__Xacc__Xinducts__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))
| c_in(V_ya,c_Wellfounded_Oacc(V_r,t_a),t_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinducts_0) ).
cnf(cls_Not__Domain__rtrancl_1,axiom,
( c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| c_in(V_x,c_Relation_ODomain(V_R,T_a,T_a),T_a) ),
file('theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
cnf(cls_acc_Oinducts_1,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ c_in(c_Pair(V_y,v_sko__Wellfounded__Xacc__Xinducts__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinducts_1) ).
cnf(cls_pair__imageI_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_A,tc_prod(T_a,T_b))
| c_in(hAPP(hAPP(V_f,V_a),V_b),c_Set_Oimage(c_split(V_f,T_a,T_b,T_c),V_A,tc_prod(T_a,T_b),T_c),T_c) ),
file('theBenchmark.p',cls_pair__imageI_0) ).
cnf(cls_DomainE_0,axiom,
( ~ c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(V_a,V_r,T_a,T_b),T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_DomainE_0) ).
cnf(cls_acc_Oinduct_0,axiom,
( ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a)
| ~ c_in(c_Pair(V_ya,v_sko__Wellfounded__Xacc__Xinduct__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))
| c_in(V_ya,c_Wellfounded_Oacc(V_r,t_a),t_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_acc_Oinduct_0) ).
cnf(cls_acc__induct_1,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_acc__induct_1) ).
cnf(cls_wf__eq__minimal_1,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(V_xa,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
file('theBenchmark.p',cls_wf__eq__minimal_1) ).
cnf(cls_Domain__iff_0,axiom,
( ~ c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(V_a,V_r,T_a,T_b),T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_Domain__iff_0) ).
cnf(cls_Image__iff_1,axiom,
( ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(V_A,V_b,V_r,T_b,T_a),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_Image__iff_1) ).
cnf(cls_Not__Domain__rtrancl_0,axiom,
( c_in(V_x,c_Relation_ODomain(V_R,T_a,T_a),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| V_x = V_y ),
file('theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
cnf(cls_Range__iff_0,axiom,
( ~ c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(V_a,V_r,T_a,T_b),V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_Range__iff_0) ).
cnf(cls_d2_I2_J_0,axiom,
v_b____ != v_a_H____,
file('theBenchmark.p',cls_d2_I2_J_0) ).
cnf(cls_d2_I1_J_0,axiom,
v_a____ != v_b_H____,
file('theBenchmark.p',cls_d2_I1_J_0) ).
cnf(cls_mem__splitI_0,axiom,
( ~ c_in(V_z,hAPP(hAPP(V_c,V_a),V_b),T_a)
| c_in(V_z,hAPP(c_split(V_c,T_b,T_c,tc_fun(T_a,tc_bool)),c_Pair(V_a,V_b,T_b,T_c)),T_a) ),
file('theBenchmark.p',cls_mem__splitI_0) ).
cnf(cls_congruent2_Ocongruent2_0,axiom,
( ~ c_Equiv__Relations_Ocongruent2(V_r1,V_r2,V_f,T_a,T_b,T_c)
| ~ c_in(c_Pair(V_y1,V_z1,T_a,T_a),V_r1,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y2,V_z2,T_b,T_b),V_r2,tc_prod(T_b,T_b))
| hAPP(hAPP(V_f,V_y1),V_y2) = hAPP(hAPP(V_f,V_z1),V_z2) ),
file('theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
cnf(cls_single__valuedD_0,axiom,
( ~ c_Relation_Osingle__valued(V_r,T_a,T_b)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_b),V_r,tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_x,V_z,T_a,T_b),V_r,tc_prod(T_a,T_b))
| V_y = V_z ),
file('theBenchmark.p',cls_single__valuedD_0) ).
cnf(cls_tfl__cut__apply_0,axiom,
( ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_R,tc_prod(T_a,T_a))
| hAPP(c_Recdef_Ocut(V_f,V_R,V_a,T_a,T_b),V_x) = hAPP(V_f,V_x) ),
file('theBenchmark.p',cls_tfl__cut__apply_0) ).
cnf(cls_cut__apply_0,axiom,
( ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| hAPP(c_Recdef_Ocut(V_f,V_r,V_a,T_a,T_b),V_x) = hAPP(V_f,V_x) ),
file('theBenchmark.p',cls_cut__apply_0) ).
cnf(cls_in__rel__def_1,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_b),V_R,tc_prod(T_a,T_b))
| c_FunDef_Oin__rel(V_R,V_x,V_y,T_a,T_b) ),
file('theBenchmark.p',cls_in__rel__def_1) ).
cnf(cls_in__rel__def_0,axiom,
( ~ c_FunDef_Oin__rel(V_R,V_x,V_y,T_a,T_b)
| c_in(c_Pair(V_x,V_y,T_a,T_b),V_R,tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_in__rel__def_0) ).
cnf(cls_trans__def_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trans__def_0) ).
cnf(cls_transD_0,axiom,
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_transD_0) ).
cnf(cls_converse__iff_1,axiom,
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_converse__iff_1) ).
cnf(cls_converseI_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(c_Pair(V_b,V_a,T_b,T_a),c_Relation_Oconverse(V_r,T_a,T_b),tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_converseI_0) ).
cnf(cls_converseD_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
| c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ),
file('theBenchmark.p',cls_converseD_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_Transitive__Closure_Otrancl__into__trancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
cnf(cls_trancl__into__trancl2_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__into__trancl2_0) ).
cnf(cls_rtrancl_Ortrancl__into__rtrancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
cnf(cls_converse__rtrancl__into__rtrancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
cnf(cls_trancl_Or__into__trancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
cnf(cls_rtrancl__trans_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_rtrancl__trans_0) ).
cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
file('theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
cnf(cls_rtrancl__eq__or__trancl_1,axiom,
c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)),
file('theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
cnf(cls_wf__asym_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_wf__asym_0) ).
cnf(cls_antisym__def_0,axiom,
( ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_x = V_y ),
file('theBenchmark.p',cls_antisym__def_0) ).
cnf(cls_antisymD_0,axiom,
( ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_a = V_b ),
file('theBenchmark.p',cls_antisymD_0) ).
cnf(cls_congruent_Ocongruent_0,axiom,
( ~ c_Equiv__Relations_Ocongruent(V_r,V_f,T_a,T_b)
| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| hAPP(V_f,V_y) = hAPP(V_f,V_z) ),
file('theBenchmark.p',cls_congruent_Ocongruent_0) ).
cnf(cls_Id__on__iff_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))
| V_x = V_y ),
file('theBenchmark.p',cls_Id__on__iff_0) ).
cnf(cls_cuts__eq_0,axiom,
( ~ c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| hAPP(V_f,V_y) = hAPP(V_g,V_y)
| c_Recdef_Ocut(V_f,V_r,V_x,T_a,T_b) != c_Recdef_Ocut(V_g,V_r,V_x,T_a,T_b) ),
file('theBenchmark.p',cls_cuts__eq_0) ).
cnf(cls_pair__in__Id__conv_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a))
| V_a = V_b ),
file('theBenchmark.p',cls_pair__in__Id__conv_0) ).
cnf(cls_Nitpick_Orefl_H__def_0,axiom,
( ~ c_Nitpick_Orefl_H(V_r,T_a)
| c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
cnf(cls_wf__irrefl_0,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_wf__irrefl_0) ).
cnf(cls_in__inv__image_1,axiom,
( ~ c_in(c_Pair(hAPP(V_f,V_x),hAPP(V_f,V_y),T_b,T_b),V_r,tc_prod(T_b,T_b))
| c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_Oinv__image(V_r,V_f,T_b,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_in__inv__image_1) ).
cnf(cls_in__inv__image_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_Oinv__image(V_r,V_f,T_b,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(hAPP(V_f,V_x),hAPP(V_f,V_y),T_b,T_b),V_r,tc_prod(T_b,T_b)) ),
file('theBenchmark.p',cls_in__inv__image_0) ).
cnf(cls_sym__def_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_sym__def_0) ).
cnf(cls_symD_0,axiom,
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_symD_0) ).
cnf(cls_rel__compI_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_c,T_b,T_c),V_s,tc_prod(T_b,T_c))
| c_in(c_Pair(V_a,V_c,T_a,T_c),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),tc_prod(T_a,T_c)) ),
file('theBenchmark.p',cls_rel__compI_0) ).
cnf(cls_r__r__into__trancl_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_R,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_R,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_r__r__into__trancl_0) ).
cnf(cls_trancl__trans_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_trancl__trans_0) ).
cnf(cls_pair__in__Id__conv_1,axiom,
c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)),
file('theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(cls_IdI_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)),
file('theBenchmark.p',cls_IdI_0) ).
cnf(cls_in__mktop_5,axiom,
( V_x = V_z
| V_x = V_y
| ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mktop_5) ).
cnf(cls_in__mktop_3,axiom,
( V_x = V_z
| V_y = V_z
| ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mktop_3) ).
cnf(cls_in__mktop_1,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_in__mktop_1) ).
cnf(cls_in__mktop_0,axiom,
~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_in__mktop_0) ).
cnf(cls_in__mktop_2,axiom,
( ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_y = V_z
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mktop_2) ).
cnf(cls_in__mkbot_4,axiom,
( c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_y = V_x
| V_x = V_y ),
file('theBenchmark.p',cls_in__mkbot_4) ).
cnf(cls_in__mkbot_1,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_in__mkbot_1) ).
cnf(cls_in__mkbot_0,axiom,
~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_in__mkbot_0) ).
cnf(cls_in__mkbot_5,axiom,
( V_y = V_z
| V_x = V_y
| ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mkbot_5) ).
cnf(cls_in__mkbot_3,axiom,
( V_y = V_z
| V_x = V_z
| ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mkbot_3) ).
cnf(cls_in__mktop_4,axiom,
( c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_xa = V_x
| V_xa = V_x ),
file('theBenchmark.p',cls_in__mktop_4) ).
cnf(cls_in__mkbot_2,axiom,
( ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_x = V_z
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_in__mkbot_2) ).
cnf(cls_complete__Lin_1,axiom,
( V_a = V_b
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_complete__Lin_1) ).
cnf(cls_1_1,axiom,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_1_1) ).
cnf(cls_1_0,axiom,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____(V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_1_0) ).
cnf(cls_mem__Sigma__iff_2,axiom,
( ~ c_in(V_a,V_A,T_a)
| ~ c_in(V_b,hAPP(V_B,V_a),T_b)
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Product__Type_OSigma(V_A,V_B,T_a,T_b),tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_mem__Sigma__iff_2) ).
cnf(cls_SigmaI_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| ~ c_in(V_b,hAPP(V_B,V_a),T_b)
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Product__Type_OSigma(V_A,V_B,T_a,T_b),tc_prod(T_a,T_b)) ),
file('theBenchmark.p',cls_SigmaI_0) ).
cnf(cls_acc__downward_0,axiom,
( ~ c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc__downward_0) ).
cnf(cls_acc_Ocases_0,axiom,
( ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_y,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_acc_Ocases_0) ).
cnf(cls_rev__ImageI_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_rev__ImageI_0) ).
cnf(cls_Image__iff_2,axiom,
( ~ c_in(V_x,V_A,T_b)
| ~ c_in(c_Pair(V_x,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a) ),
file('theBenchmark.p',cls_Image__iff_2) ).
cnf(cls_Id__on__iff_1,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))
| c_in(V_x,V_A,T_a) ),
file('theBenchmark.p',cls_Id__on__iff_1) ).
cnf(cls_Id__on__eqI_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_Id__on__eqI_0) ).
cnf(cls_equiv__class__eq__iff_2,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_2) ).
cnf(cls_equiv__class__eq__iff_1,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,V_A,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_1) ).
cnf(cls_Range__iff_1,axiom,
( ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
file('theBenchmark.p',cls_Range__iff_1) ).
cnf(cls_RangeI_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_b,c_Relation_ORange(V_r,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_RangeI_0) ).
cnf(cls_Domain__iff_1,axiom,
( ~ c_in(c_Pair(V_a,V_x,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
file('theBenchmark.p',cls_Domain__iff_1) ).
cnf(cls_DomainI_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
file('theBenchmark.p',cls_DomainI_0) ).
cnf(cls_SigmaD2_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),c_Product__Type_OSigma(V_A,V_B,T_a,T_b),tc_prod(T_a,T_b))
| c_in(V_b,hAPP(V_B,V_a),T_b) ),
file('theBenchmark.p',cls_SigmaD2_0) ).
cnf(cls_SigmaD1_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),c_Product__Type_OSigma(V_A,V_B,T_a,T_b),tc_prod(T_a,T_b))
| c_in(V_a,V_A,T_a) ),
file('theBenchmark.p',cls_SigmaD1_0) ).
cnf(cls_total__on__def_0,axiom,
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_xa,V_A,T_a)
| V_x = V_xa
| c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_total__on__def_0) ).
cnf(cls_refl__on__def_1,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_refl__on__def_1) ).
cnf(cls_refl__onD2_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ),
file('theBenchmark.p',cls_refl__onD2_0) ).
cnf(cls_refl__onD1_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,V_A,T_a) ),
file('theBenchmark.p',cls_refl__onD1_0) ).
cnf(cls_refl__onD_0,axiom,
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('theBenchmark.p',cls_refl__onD_0) ).
cnf(cls_d1_I2_J_0,axiom,
v_a_H____ != v_b_H____,
file('theBenchmark.p',cls_d1_I2_J_0) ).
cnf(cls_Pair__eq_1,axiom,
( V_b = V_b_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('theBenchmark.p',cls_Pair__eq_1) ).
cnf(cls_Pair__eq_0,axiom,
( V_a = V_a_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('theBenchmark.p',cls_Pair__eq_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(V_S,V_x))
| c_in(V_x,V_S,T_a) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(cls_mem__def_0,axiom,
( ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(cls_CHAINED_0,axiom,
c_in(v_Q____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_CHAINED_3,axiom,
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_xa,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_x,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_xa,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_xa),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_3) ).
cnf(cls_CHAINED_2,axiom,
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_xa,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_x,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_xa,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_xa),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_2) ).
cnf(cls_CHAINED_1,axiom,
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_xa,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_x,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_xa,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_xa),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_1) ).
cnf(cls_CHAINED_0_02,axiom,
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_xa,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_x,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_xa,v_sko__CHAINED__1(V_a,V_b,V_x,V_xa)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_xa),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_0_02) ).
cnf(cls_CHAINED_1_03,axiom,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_1_03) ).
cnf(cls_CHAINED_0_04,axiom,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_Q____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_CHAINED_0_04) ).
cnf(cls_CHAINED_0_05,axiom,
c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_Q____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_CHAINED_0_05) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olower__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( ~ class_Lattices_Odistrib__lattice(T_1)
| class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( ~ class_Lattices_Obounded__lattice(T_1)
| class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( ~ class_Lattices_Oboolean__algebra(T_1)
| class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( ~ class_Orderings_Opreorder(T_1)
| class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( ~ class_Orderings_Oorder(T_1)
| class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( ~ class_Orderings_Obot(T_1)
| class_Orderings_Obot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( ~ class_HOL_Oord(T_1)
| class_HOL_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__HOL_Oord) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ c_fequal(V_X,V_Y,T_a)
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_in__mktop_4_simplified,plain,
( c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_xa = V_x ),
inference(simplify_clause,[status(thm)],[cls_in__mktop_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Oupper__semilattice__class_Osup(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Olower__semilattice__class_Oinf(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Orderings_Obot__class_Obot(Eq_x_0) = c_Orderings_Obot__class_Obot(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_Relation_OImage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Relation_OImage(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_List_Osko__Recdef__Xtfl__wf__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osko__Recdef__Xtfl__wf__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Set_Oinsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Oinsert(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_COMBK(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBK(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_HOL_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Ominus__class_Ominus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Set_Oimage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Set_Oimage(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_HOL_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_HOL_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Product__Type_OSigma(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_OSigma(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Relation_ODomain(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ODomain(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Relation_ORange(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_ORange(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_Transitive__Closure_Ortrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_Pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Pair(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Relation_Oconverse(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_Oconverse(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_Relation_Orel__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Relation_Orel__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_List_Osko__Recdef__Xcuts__eq__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_List_Osko__Recdef__Xcuts__eq__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Recdef_Ocut(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Recdef_Ocut(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_Relation_OId(Eq_x_0) = c_Relation_OId(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( c_ATP__Linkup_Osko__Relation__XImageE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Relation__XImageE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_Wellfounded_Oacc(Eq_x_0,Eq_x_1) = c_Wellfounded_Oacc(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( c_Transitive__Closure_Otrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otrancl(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( c_Relation_OId__on(Eq_x_0,Eq_x_1) = c_Relation_OId__on(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(Eq_x_0,Eq_x_1,Eq_x_2) = v_sko__Transitive__Closure__Xrtrancl__Xcases__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( v_sko__Transitive__Closure__Xtrancl__Xcases__1(Eq_x_0,Eq_x_1,Eq_x_2) = v_sko__Transitive__Closure__Xtrancl__Xcases__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( c_ATP__Linkup_Osko__Relation__XIdE__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Relation__XIdE__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( c_ATP__Linkup_Osko__Relation__XId__onE__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Relation__XId__onE__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(Eq_x_0,Eq_x_1) = c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( c_split(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_split(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( v_sko__Wellfounded__Xacc__Xinducts__1(Eq_x_0,Eq_x_1) = v_sko__Wellfounded__Xacc__Xinducts__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( c_Relation_Oinv__image(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Relation_Oinv__image(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( v_sko__Wellfounded__Xacc__Xinduct__1(Eq_x_0,Eq_x_1) = v_sko__Wellfounded__Xacc__Xinduct__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( c_ATP__Linkup_Osko__Relation__XRangeE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Relation__XRangeE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( c_ATP__Linkup_Osko__Relation__XDomainE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Relation__XDomainE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( c_Arrow__Order__Mirabelle_Omktop(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omktop(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( c_Arrow__Order__Mirabelle_Omkbot(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omkbot(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(Eq_x_0,Eq_x_1) = v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( v_P____(Eq_x_0) = v_P____(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( v_F(Eq_x_0) = v_F(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( v_sko__CHAINED__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = v_sko__CHAINED__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( class_Lattices_Odistrib__lattice(Eq_y_0)
| ~ class_Lattices_Odistrib__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( c_Wellfounded_Owf(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_Owf(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( class_Lattices_Oupper__semilattice(Eq_y_0)
| ~ class_Lattices_Oupper__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( class_OrderedGroup_Oab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Oab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_lessequals(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( class_Lattices_Olattice(Eq_y_0)
| ~ class_Lattices_Olattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( class_Lattices_Olower__semilattice(Eq_y_0)
| ~ class_Lattices_Olower__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,axiom,
( c_Wellfounded_Oacyclic(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_Oacyclic(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,axiom,
( c_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_in(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,axiom,
( class_OrderedGroup_Opordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,axiom,
( class_Orderings_Obot(Eq_y_0)
| ~ class_Orderings_Obot(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( c_Relation_Osym(Eq_y_0,Eq_y_1)
| ~ c_Relation_Osym(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( class_Lattices_Obounded__lattice(Eq_y_0)
| ~ class_Lattices_Obounded__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,axiom,
( c_Relation_Orefl__on(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Orefl__on(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,axiom,
( c_Relation_Otrans(Eq_y_0,Eq_y_1)
| ~ c_Relation_Otrans(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,axiom,
( class_OrderedGroup_Ogroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ogroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_94,axiom,
( c_Relation_Ototal__on(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Ototal__on(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_95,axiom,
( c_Order__Relation_Ostrict__linear__order__on(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Order__Relation_Ostrict__linear__order__on(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_96,axiom,
( class_OrderedGroup_Olordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,axiom,
( c_Equiv__Relations_Oequiv(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Equiv__Relations_Oequiv(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_98,axiom,
( c_Relation_Oirrefl(Eq_y_0,Eq_y_1)
| ~ c_Relation_Oirrefl(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_99,axiom,
( c_Relation_Oantisym(Eq_y_0,Eq_y_1)
| ~ c_Relation_Oantisym(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,axiom,
( c_Relation_Osingle__valued(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Relation_Osingle__valued(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( c_Nitpick_Orefl_H(Eq_y_0,Eq_y_1)
| ~ c_Nitpick_Orefl_H(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_102,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( class_HOL_Oord(Eq_y_0)
| ~ class_HOL_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( c_Equiv__Relations_Ocongruent(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Equiv__Relations_Ocongruent(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( c_Equiv__Relations_Ocongruent2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ c_Equiv__Relations_Ocongruent2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( c_FunDef_Oin__rel(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ c_FunDef_Oin__rel(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( c_fequal(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_fequal(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT040-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 19 21:07:19 UTC 2026
% 0.12/0.38 % CPUTime :
% 183.15/183.47 % SZS status Unsatisfiable for theBenchmark
% 183.15/183.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------